Since quadrilateral MATH has opposite sides congruent and parallel, it is a parallelogram.
In a parallelogram, opposite sides are parallel and congruent, but the opposite angles are also congruent.
Therefore, we can say that angle M is congruent to angle H, and angle A is congruent to angle T.
Option A states that MT is congruent to AH, which is not always true for a parallelogram.
Option B states that MT is perpendicular to AH, which is also not always true for a parallelogram.
Option C states that angle MHT is congruent to angle ATH. Since angle M is congruent to angle H and angle A is congruent to angle T, we can say that angle MHT is congruent to angle ATH. This is always true for a parallelogram, as opposite angles are congruent.
Option D states that angle MAT is congruent to angle MHT. This is not always true for a parallelogram. While angle MHT is congruent to angle ATH (as explained in Option C), there is no reason to assume that angle MAT is congruent to angle MHT.
Therefore, the correct answer is: C. Angle MHT is congruent to Angle ATH.
If the sun is 59 degrees above the horizon, find the length of the shadow cast by a building 52 feet tall, round your answer to the nearest tenth
Answer:44.5
Step-by-step explanation:
To solve this problem, we can use the tangent function, which relates the angle of elevation to the length of the opposite side (the shadow) and the adjacent side (the height of the building).Let x be the length of the shadow.
Then, we have:tan(59°) = 52/xTo solve for x, we can cross-multiply and simplify:x = 52 / tan(59°)
x ≈ 44.5 feet (rounded to the nearest tenth)Therefore, the length of the shadow cast by the building is approximately 44.5 feet.
What is the conversion of 21 km to miles ?
The conversion of 21 km to miles is 13.04848 miles.
Kilometer (km) and mile are both units of measurement used to express distance or length.
Kilometer is a metric unit of distance commonly used in the International System of Units (SI) and is equal to 1000 meters.
To convert 21 kilometers (km) to miles, we can use the conversion factor of 1 km = 0.621371192 miles.
So, we can multiply 21 km by 0.621371192 miles/km to get the equivalent distance in miles:
21 km × 0.621371192 miles/km = 13.04848 miles (rounded to five decimal places)
Therefore, 21 km is approximately equal to 13.04848 miles.
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he - Venn diegram below describes the probablity of students who wlll lake Chem istry = and Spanish at Jafferson High School next year; Where A Student takes chemistry and B Students takes Spanish_ Suppose one student Is chosen at random Use Ihe above vann dlagram . Find the value of P(A L 8) and describe In words. a.) 0.6; The probability that the student takes both chemistry and Spanish. b.) 0.1; The probability that the student takes both chemistry and Spanish_ c.) 0.1; The probability that the student takes either chemistry or Spanish; bul not both. d.)0.6; The probability that the student takes either chemistry or Spanish, or both.
From the Venn diagram , the value of required probability P(A∪B) is given by :
Option a). 0.6 . The probability that students takes both Spanish and Chemistry.
Let us consider 'A' be the probability of the students who takes Chemistry.
And 'B' be the probability of the students who takes Spanish.
From the Venn diagram we have,
Probability of A 'P(A) ' = 0.2 + 0.1
= 0.3
Probability of B 'P(B)' = 0.3 + 0.1
= 0.4
Probability of A∩B 'P(A∩B)' = 0.1
Probability of A∪B is given by :
P(A∪B) = P(A) + P(B) - P(A∩B)
Substitute the value we get ,
⇒ P(A∪B) = 0.3 + 0.4 - 0.1
⇒ P(A∪B) = 0.6
P(A∪B) represents the probability of the students that takes both Chemistry and Spanish.
Therefore, the value and explanation of P(A∪B) is equal to :
Option a). 0.6 , the probability of the students that takes both Chemistry and Spanish.
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The above question is incomplete , the complete question is:
The - Venn diagram below describes the probability of students who will take Chemistry and Spanish at Jefferson High School next year, where A Student takes chemistry and B Students takes Spanish. Suppose one student is chosen at random Use the attached Venn diagram .
Find the value of P(A∪B) and describe in words.
a.) 0.6; The probability that the student takes both chemistry and Spanish.
b.) 0.1; The probability that the student takes both chemistry and Spanish.
c.) 0.1; The probability that the student takes either chemistry or Spanish; but not both.
d.)0.6; The probability that the student takes either chemistry or Spanish, or both.
Venn diagram is attached.
for a period of time, an island's population grows exponentially. If the population doubles every 34 years and the current population is 1233, what will the population be 6 years from now?
As a result, the island's population will be about 1397.33 persons in 6 years.
What is exponent?An exponent, also called a power or index, is a mathematical operation that indicates the number of times a base number is multiplied by itself. Exponents are written as a superscript number to the right of the base number. Exponents can be positive or negative, and they can be whole numbers or fractions. A positive exponent tells us to multiply the base number by itself, while a negative exponent tells us to divide the base number into 1. Exponents can be used to simplify and solve many mathematical problems, and they are an important part of many areas of mathematics, including algebra, calculus, and geometry.
Here,
If the population of the island doubles every 34 years, we can use the exponential growth formula to determine the population after a certain period of time:
P = P0 * 2ⁿ÷³⁴
where P is the population after time t, P0 is the initial population, and t is the time elapsed in years.
We know that the current population is 1233, so P0 = 1233. We want to find the population 6 years from now, so t = 6. Plugging these values into the formula, we get:
P = 1233 * 2⁶÷³⁴
P ≈ 1397.33
Therefore, the population of the island will be approximately 1397.33 people 6 years from now.
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Find the value of each markup or discount. 1. original $10.00 percent of markup: 20%
The value of the markup is $12
How to determine the value of the markupFrom the question, we have the following parameters that can be used in our computation:
Original $10.00 percent of markup: 20%
The markup price is calculated as
Markup Price = Original; * (1 + Markup)
Substitute the known values in the above equation, so, we have the following representation
Markup Price = 10 * (1 + 20%)
Evaluate
Markup Price = 12
Hence, the price is $12
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Use the diagram to complete the statements.
The angle of depression from point R to point S is angle
.
The angle of elevation from point S to point R is angle
.
Angle 2 is the angle of elevation from
.
Angle 1 is the angle of
.
The angle of depression from point R to point S is ∠1.
The angle of elevation from point S to point R is ∠2.
∠2 is the angle of elevation from S to R.
∠1 is the angle of depression from point R to point S.
What is an angle of depression?
If the line of sight is directed downward from the horizontal line, then an angle is created with the horizontal line. The angle formed between the horizontal line and the observer's line of sight is known as the angle of depression if the object being observed is below the observer's level.
There is an angle of elevation from point R to S. Thus point R is lie above S.
The angle of depression from point R to point S is ∠1.
The angle of elevation from point S to point R is ∠2.
∠2 is the angle of elevation from S to R.
∠1 is the angle of depression from point R to point S.
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Graph the following function: G(x)=3/4•2^x
You can do this on the desmos graph
The GDP deflator formula can be used in a variety of ways. Use it to answer the questions that follow. Round final answers to two decimal places, as needed
The nominal GDP in 2012 is $3,450.00.
The GDP deflator is a price index that measures the average price level of goods and services produced in an economy. It is calculated as the ratio of nominal GDP to real GDP, multiplied by 100.
Nominal GDP (Gross Domestic Product) is a measure of the total value of all goods and services produced within a country's borders during a given period of time, usually a year, using current market prices
To use the GDP deflator formula to answer the question, we need to rearrange the formula and solve for nominal GDP:
Nominal GDP = Real GDP × (GDP deflator / 100)
Plugging in the given values, we get:
Nominal GDP = $2,300.00 × (150.00 / 100) = $3,450.00
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The given question is incomplete, the complete question is:
: The GDP deflator formula can be used in a variety of ways. Use it to answer the questions that follow. Round final answers to two decimal places, as needed. Real GDP $2300.00 GDP deflator 150.00 .what is the nominal GDP in 2012 ?
Please help me now this is due
The area below the curve is equal to 10 - 3π / 2 square units. (Correct choice: B)
How to determine the area below a curve
In this problem we need to determine the area below the curve for the interval x ∈ [- 4, 7]. Mathematically speaking, this area can be found by means of definite integrals. Given that we find a piecewise function formed by five expressions, the area is the sum of several subintervals.
The areas can be represented by using the following area formulas:
Triangle
A = 0.5 · w · l
Semicircle
A = 0.5π · R²
Rectangle
A = w · l
Where:
w - Widthl - LengthR - RadiusPlease notice the area above the x-axis is positive and the area below the x-axis is negative. Finally, we find the net area below the curve:
A = 0.5 · 2 · 2 - 0.5π · 2² + 0.5 · 2 · 2 + 2 · 2 + 0.5π · 1² + 1 · 2
A = 2 - 2π + 2 + 4 + 0.5π + 2
A = 10 - 1.5π
A = 10 - 3π / 2
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You have a combination lock with 3 secret digits. Find the 3 correct digits using the following clues and enter your answer below.
Answer: The correct digits for the combination lock are 1, 5, and 8, in that order.
Step-by-step explanation:
Based on the given clues, we can deduce the correct digits for the combination lock as follows:
From the clue "128 One digit is right and in its place," we know that one of the digits is 1.
From the clue "157 One digit is right, but in the wrong place," we know that either 5 or 7 is a correct digit, but in the wrong position. Since we already know that one of the digits is 1, the correct digit must be 5. Therefore, the second digit is 5 and it is in the wrong place.
From the clue "841 Two digits are right but both are in the wrong place," we know that the digits 8 and 4 are correct, but they are both in the wrong position. Therefore, the last digit must be 4 or 8. However, we also know from the clue "624 One digit is right, but in the wrong place" that the last digit is not 4. Therefore, the correct third digit is 8.
So, the correct digits for the combination lock are 1, 5, and 8, in that order.
Therefore, the combination for the lock is 158.
What multiplies to 6 and adds to negative 4
Answer:
-2+sqrt(2)i and -2-sqrt(2)i
Step-by-step explanation:
use system of equations
xy = 6
x+y=-4
(-4-y)y=6
-y^2 -4y + 6 = 0
Use quadratic formula
y = -2 ± sqrt(2)i
Now substitute
x + (-2 ± sqrt(2)i) = -4
X = -4-(-2±sqrt(2)i) = -2±sqrt(2)i
are you sure you typed the question right?
simplify and distribute 5h^3(4h^2-7h)
20h⁵ - 35h⁴ is the simplified and dispersed expression.
What does math's distribution mean?
Something is divided, shared, or given away when it is "distributed." What does this mean for the distributive property of mathematics? Basic arithmetic operations like addition and subtraction are used to divide the results of multiplication according to the distributive property of the law of multiplication.
We may utilize the distributive property of multiplication, which asserts that a(b + c) = ab + ac, to distribute and simplify 5h³(4h² - 7h).
The 5h³ is first distributed to both words inside of the parenthesis as follows:
5h³(4h² - 7h) is equal to 5h³ * 4h² - 5h³ * 7h.
Secondly, by multiplying the coefficients and adding the exponents, we simplify each term:
20:5 + 5:3 + 4:2 + 5:3 + 7:4 = 35:4
When we add everything together, we get the following: 5h³(4h² - 7h) = 20h⁵- 35h⁴.
Hence, 20h⁵ - 35h⁴ is the simplified and dispersed expression.
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what is linear interpolation formula
The formula of linear interpolation(y) = [tex]y_{1} +\frac{(x - x_{1}) (y_{2} -y_{1}) }{x_{2} -x_{1} }[/tex]
The formula to calculate linear interpolation is:
Linear Interpolation(y) = [tex]y_{1} +\frac{(x - x_{1}) (y_{2} -y_{1}) }{x_{2} -x_{1} }[/tex]
where,
[tex]x_{1}[/tex] and [tex]y_{1}[/tex] are the first coordinates[tex]x_{2}[/tex] and [tex]y_{2}[/tex] are the second coordinatesx is the point to perform the interpolationy is the interpolated value.It allows users to interpolate (interpolation is a mathematical technique for estimating any value between two known points) data points between the sets(two sets) of points or coordinates.
Take the two known points and calculate the value of the point that lies between them. This has been used in as many engineering applications as estimating the value of a point on a graph or table. This calculator helps in estimating the value of a point that lies between two known points on a line.
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what issquare root 12
The square root of 12 is approximately 3.464. To calculate the square root of 12, you can use a calculator or manually by using long division or the Babylonian method.
The Babylonian method involves making an initial guess, dividing the number by the guess, averaging the result with the guess, and repeating the process until the desired level of accuracy is achieved. In this case, the process would look like this:
Start with an initial guess, say 3.Divide 12 by 3 to get 4.Average 3 and 4 to get 3.5.Divide 12 by 3.5 to get 3.42857.Average 3.5 and 3.42857 to get 3.46428.Repeat the process until the desired level of accuracy is achieved.
The square root of 12 is an irrational number, which means it cannot be expressed as a fraction and its decimal representation goes on forever without repeating.
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at a certain time of day, the angle of elevation of the sun is 44 degrees. find the length of the shadow cast by a building 30 meters high.
The length of the shadow casted by the building is 31.06 meters. The solution has been obtained by using trigonometry.
What is trigonometry?
Trigonometry is a discipline of mathematics that deals with the study of sides, angles, and relationships in triangles.
We are given that at a certain time of day, the angle of elevation of the sun is 44 degrees. The height of the building is given as 30 meters.
Using trigonometry,
We know that tan theta = opposite side/ adjacent side
So,
⇒tan 44° = 30/x
⇒0.9657 = 30/x
⇒x = 31.06
Hence, the length of the shadow casted by the building is 31.06 meters.
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how to determine the sum of all the factors of 100
Answer:
5, 10 20, etc.
Step-by-step explanation:
You can skip count like you do in multiplying.
calculate 10% of 360km
Answer:36
Step-by-step explanation:360 * 0.1 = 36 or 360/10 = 36
(1/512)^1/3
I know the answer is 1/8 but how do I get to that?
Answer:
See explanation below
Answer is 1/8
Step-by-step explanation:
The expression is:
[tex]\left(\dfrac{1}{512}\right)^{\dfrac{1}{3}}[/tex]
A number x raised to the power [tex]\dfrac{1}{3}[/tex] means it is the cube root of that number or [tex]\mbox{\large \sqrt[3]{x} }[/tex]
Also [tex]\left(\dfrac{1}{x}\right)^a = \dfrac{(1)^a}{x^a}[/tex]
Combining these two facts we get
[tex]\left(\dfrac{1}{512}\right)^{\frac{1}{3}} = \dfrac{1^{\frac{1}{3}}}{512^\frac{1}{3}}= \dfrac{\sqrt[3]{1} }{\sqrt[3]{512} } = \dfrac{1}{\sqrt[3]{512} }[/tex]
[tex]\sqrt[3]{512} = 8[/tex]
So
[tex]\left(\dfrac{1}{512}\right)^{\dfrac{1}{3}} = \dfrac{1}{8}[/tex]
2/3(3-6x)=-3(8x-4).
Answer:
x = [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Solve for x
[tex]\frac{2}3}(3-6x)=-3(8x-4)[/tex]
Distribute [tex]\frac{2}{3}[/tex] and -3.
[tex]2-4x=-24x+12[/tex]
Simplify
[tex]-4x+2=-24x+12[/tex]
Subtract 2 on both sides
[tex]-4x=-24x+10[/tex]
Subtract -24x on both sides
[tex]20x=10[/tex]
Divide by 20
[tex]x=\frac{1}{2}[/tex] or 0.5
Write a quadratic function with zeroes 0 and – 7. Write your answer using the variable x and in standard form with a leading coefficient of 1.
This is the standard form of a quadratic function with leading coefficient 1, and 0 and -7.
If the zeros of a quadratic function are 0 and -7, then the function can be written as:
f(x) = a(x - 0)(x - (-7))
Simplifying:
f(x) = a(x)(x + 7)
To find the value of 'a', we can use one of the points on the parabola. Since we know that the x-intercept is 0, we can substitute x = 0 and y = 0 into the equation:
0 = a(0)(0 + 7)
0 = 0
This tells us that a can be any value, as long as it's not 0. Let's choose a = 1 for simplicity. Then the quadratic function with zeros 0 and -7 is:
f(x) = (x)(x + 7)
f(x) = x^2 + 7x
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Find the missing length. The triangles in each pair are similar.
Answer: 56
Step-by-step explanation: Since we know both triangles are similar, we want to first find the scale factor between the two triangles, knowing side UP and side PQ are corresponding we can find that 84/60 or in simplified terms, 7/5 is the scale factor. Now we know that side VP and side PR are corresponding so 40 x 7/5 gives us 56 which is side PR. Hope this helped! :)
Find the length of X
Answer:
Below
Step-by-step explanation:
21 is to 27 as x-3 is to x-1
21/27 = x-3/x-1 cross multipliy , solve for x = 10
Answer:
x = 10Step-by-step explanation:
x-3/21 = x-1/27
27(x-3) = 21(x-1)
27x-81 = 21x-21
27x-21x = -21+8
6x = 60
x = 60/6
x = 10
_____________________
Hope this helps! :)
kyle and ryan take entrance exams at two different universities. kyle scores a 403 on an exam with a mean of 355 and a standard deviation of 59, while ryan scores a 45 on an exam with a mean of 27 and a standard deviation of 4. which do you think is more likely to be accepted at the university of his choice?
Therefore, based on their z-scores, Ryan is more likely to be accepted at his university of choice than Kyle, assuming that the admissions decision is based solely on their exam scores.
What is probability?Probability is a measure of the likelihood or chance of an event occurring. It is a numerical value between 0 and 1, where 0 means that the event is impossible and 1 means that the event is certain to occur. The closer the probability is to 1, the more likely the event is to occur, while the closer it is to 0, the less likely it is to occur.
Here,
To determine which of the two students is more likely to be accepted at their university of choice, we need to compare their exam scores relative to the other students who took the same exam. We can use the concept of standard scores, also known as z-scores, to make this comparison.
The z-score of an observation x is the number of standard deviations that x is away from the mean of the population. It is calculated as:
z = (x - μ) / σ
where x is the observation, μ is the mean of the population, and σ is the standard deviation of the population.
For Kyle's exam, his z-score is:
z = (403 - 355) / 59 = 0.814
For Ryan's exam, his z-score is:
z = (45 - 27) / 4 = 4.5
A z-score of 0 means the observation is at the mean of the population, while a positive z-score means the observation is above the mean, and a negative z-score means the observation is below the mean.
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5. A population of bumble bees starts at 20 bees in the spring. Every week, the
population of bumble bees triples. Write the geometric sequence formula and
find the number of bees after 32 weeks. Show all of your work.
After 32 weeks, the population of bumble bees will be 6.77315 x 10¹⁴ bees.
Solving for the population of bumble bees after 32 weeks:The population of bumble bees triples every week, so the common ratio is 3. The starting population is 20 bees.
The formula for a geometric sequence is:
a_n = a_1 * rⁿ⁻¹
where,
a_n = the nth term in the sequence
a_1 = the first term
r = the common ratio
n = the number of terms.
Using this formula, we can find the number of bees after 32 weeks:
a_32 = 20 * 3³²⁻¹
a_32 = 20 * 3³¹
a_32 = 6.773150 × 10¹⁴
Therefore, after 32 weeks, the population of bumble bees will be approximately 6.77315 x 10¹⁴ bees.
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Write each phrase as an algebraic expression.
14. n divided by 8.
15. p multiplied by 4
16. b plus 14.
17. 90 times x,
18. a take away 16.
19. k less than 24
20. 3 groups of w
21. the sum of 1 and q
22. the quotient of 13 and z.
23. cadded to 45
Each phrase can be epressed as an algebraic expression as:
n/8
4p,
b+14
90x
-16
24-k
3(w)
1+q
13/z
45+c
w-8
What is algebraic expression?An expression that uses constant algebraic numbers, variables, and algebraic operations is known as an algebraic expression in mathematics (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number). A good example of an algebraic expression is 3x2 2xy + c.
A variable expression can be described using its terms and operations on the terms as an algebraic expression. For instance, "3 more than x" can be used to describe x + 3.
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what is 56 as a decimal?
Answer: 56 as a decimal is 0.56
Step-by-step explanation: Just simply add a decimal point in front of 56, and you’ll get 0.56
56 = 0.56
Hope this helps!
In a certain triangle, the measure of angle A is three times as big as the measure of angle C and the measure of angle B is 30 degrees bigger than the measure of angle C. What is the degree measure of angle A
The degree measure of angle A is 90 degrees if the measure of angle A is three times as big as the measure of angle C and the measure of angle B is 30 degrees bigger than the measure of angle C.
Let x be the measure of angle C in degrees.
According to the problem statement, angle A is three times as big as angle C, measuring 3x degrees.
Angle B is 30 degrees bigger than angle C, so its measure is x + 30 degrees.
The sum of the measures of the angles in a triangle is always 180 degrees so that we can write:
A + B + C = 180
Substituting the expressions we found for the angles in terms of x, we get:
3x + (x + 30) + x = 180
Simplifying and solving for x, we get:
5x + 30 = 180
5x = 150
x = 30
Therefore, angle C has a measure of 30 degrees, angle B has an estimate of 30 + 30 = 60 degrees, and angle A has a measure of 3(30) = 90 degrees.
So the degree measure of angle A is 90 degrees.
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what is the quotient of 25 divide by 25,704 use long division
The quotient of 25 divided by 25,704 is approximately 0.00097 (rounded to five decimal places).
How would one describe long division?When splitting huge numbers, the task is divided into several sequential steps using the long division approach. The dividend is divided by the divisor, just like in conventional division problems, and the result is known as the quotient; occasionally, it also produces a remainder.
The long division for 25 divided by 25,704 is shown below:
code :
0.00097
-------
25704 | 25.00000
0
--
250
257
---
-7
As a result, the result of 25 divided by 25,704 is almost 0.00097. (rounded to five decimal places).
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HELP PLEASEEE
Write en equation of a Line that goes through (1, 2) slope = 7. Put in point slope
A group of friends wants to go to the amusement park. They have $86 to spend on parking and admission. Parking is $5, and tickets cost $13.50 per person, including tax. Write and solve an equation which can be used to determine
�
x, the number of people who can go to the amusement park.
Equation:
Answer x =
The maximum number of people who can go to the amusement park is 6.
How to find maximum number?To determine the number of people who can go to the amusement park, use the following equation:
Total cost = Parking cost + Admission cost
The total cost cannot exceed $86, the amount of money the friends have. The parking cost is $5 and the admission cost per person is $13.50. Therefore, we can write the following equation:
86 ≥ 5 + 13.5x
To solve for x, subtract 5 from both sides of the inequality and then divide both sides by 13.5. This gives us the following equation:
x ≤ (86 - 5) / 13.5
x ≤ 6
Therefore, the maximum number of people who can go to the amusement park is 6.
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